### If f is continuous and integral from 0 to 9 f(x)dx=4

The aim of this question is to find the integral of a given expression. Furthermore, the upper and lower limits of the integral are also given, i.e., we have a definite integral in this question. This question is based on the concept of arithmetic. The integral tells us about the area under the curve. Furthermore, […]

### 8 and n as factors, which expression has both of these?

This question aims to find an expression that has both the given factors. Moreover, it is helpful to have a number divisible by the given numbers. This question is based on the concepts of arithmetic, and the factors of a number include all divisors of that specific number. The factors of the number 16, for […]

### The amount of time Ricardo spends brushing his teeth follows a normal distribution with unknown mean and standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and standard deviation of this distribution.

The question aims to find the mean $mu$ and standard deviation $sigma$ of a standard normal distribution. In arithmetic, a standard score is the number of standard deviations where the maturity of the observed point is above or below the average value of what is observed or measured. Raw scores above the mean generally have […]

### Assume that a procedure yields a binomial distribution.

With n=6 trials and a probability of success of p=0.5 . Use a binomial probability table to find the probability that the number of successes x is exactly 3. The target of this question is to find the probability using a binomial distribution table. With the given number of trials and probability of success, the […]

### Prove or disprove that if a and b are rational numbers, then a^b is also rational.

The main objective of this question is to prove or disprove that $a^b$ is a rational number provided that $a$ and $b$ are rational numbers. In arithmetic, a rational number is a number that can be expressed as the ratio $dfrac{a}{b}$ of two integers such that $b neq 0$. Apart from fractions, the set of rational numbers […]